Calculation of the acoustic radiation field at the surface of a finite cylinder by the method of weighted residuals

In the design of sonar systems it is desirable to compute the acoustic radiation field at the transducer surface, upon which all the significant radiation properties (radiation impedance, beam patterns, etc.) depend. Like other practical array geometries of interest, the finite cylinder does not belong to the class of separable coordinate surfaces of the Helmholtz equation, and consequently, the acoustic field for this geometry cannot be determined analytically. In this paper the surface field is computed numerically from the interior Helmholtz integral equation by the method of weighted residuals. Since the pressure fields over the three surfaces of the finite cylinder must coincide along the locii of intersection between the cylindrical surface and the end caps, the interior Helmholtz integral equation must he constrained to meet this requirement. The matrix representation of this equation which is not self-adjoint is solved by the method of least squares. This enables the constraints to be introduced via Lagrange multipliers. The procedure is used to calculate the surface pressure and radiation impedance of the finite cylinder for a range of axis ratios (diameter/length) and frequencies of interest in sonar applications. Calculations of the radiation resistance and the directivity index determined in this manner are shown to differ from those previously evaluated from the far-field solution. The weighted-residual methods considered are shown to have excellent convergence properties which make them more versatile than alternative numerical methods for solving the problem.